University of Groningen On the nature of the coefficient of ......although no experimental validation has been provided yet. Therefore, the aim of this work is to give an experimental

University of Groningen

On the nature of the coefficient of friction of diamond-like carbon films deposited on rubberMartinez-Martinez, D.; van der Pal, J. P.; Schenkel, M.; Shaha, K. P.; Pei, Y. T.; De Hosson,J. Th. M.Published in:Journal of Applied Physics

DOI:10.1063/1.4723830

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https://doi.org/10.1063/1.4723830

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https://doi.org/10.1063/1.4723830

On the nature of the coefficient of friction of diamond-like carbon filmsdeposited on rubber

D. Martinez-Martinez,a) J. P. van der Pal, M. Schenkel, K. P. Shaha, Y. T. Pei,a)

and J. Th. M. De HossonDepartment of Applied Physics, Materials innovation institute M2i, University of Groningen,Nijenborgh 4, Groningen, 9747 AG, The Netherlands

(Received 25 January 2012; accepted 2 May 2012; published online 1 June 2012)

In this paper, the nature of the coefficient of friction (CoF) of diamond-like carbon (DLC)-protected

rubbers is studied. The relative importance of the viscoelastic and adhesive contributions to the

overall friction is evaluated experimentally by modifying the contact load and the adhesive strength

between the surface and the counterpart. The results indicate that the increase of CoF during the

tribotests under non-lubricated conditions is caused by the increase of the adhesive contribution to

friction motivated by the growth of the contact area during the test. In the case of oil lubricating

condition, the adhesive force is minimized and the CoF is observed to decrease during the tribotest.

This is caused by the reduction of the viscoelastic contribution due to the variation of the shape of the

contact area. The role of the microstructure of the DLC film on the efficiency of the oil lubrication is

also discussed.VC 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4723830]

I. INTRODUCTION

Diamond-like carbon (DLC) films are attractive solu-

tions as protective coatings for many applications, due to the

combination of relatively high hardness, chemical inertness,

low friction, and low wear rate.1,2 Their chemical composi-

tion, which is mainly composed of C and H, suggests a good

compatibility with rubber materials. Rubber seals are incor-

porated in ball bearings widely used in many technical fields,

like aerospace and automotive industries,3 in order to prevent

the leakage of lubricant and the entrance of dirt. However,

under operation dynamic rubber seals suffer from severe

wear and cause high friction, leading to an ultimate failure of

the bearings. Therefore, a protective coating with optimal tri-

bological performance is of interest regarding energy saving

and environmental protection.

The deposition of DLC films by plasma enhanced chem-

ical vapor deposition (PECVD) has demonstrated to be a

good choice for the protection of flexible substrates.4–11 In

previous papers, we reported the deposition of self-

segmented DLC films, which improves film flexibility with-

out reduction of tribological performance.8–11 These films

showed an excellent adhesion to the substrate, and the pro-

tected rubbers demonstrated negligible wear and much lower

CoF than the corresponding unprotected specimens.10 Thus,

no debris formation or adhesive failure was detected in the

films during the tribotests. In addition, the CoF could be con-

trolled by a proper tailoring of the film microstructure by a

proper selection of the temperature differences during film

growth (DT).8,9

In all cases, the friction coefficient follows a similar trend

when the number of cycles of the tribotest is increased (see

Figure 2 as an example): the CoF progressively grows until a

steady state is finally reached. The number of laps needed to

achieve this steady state depends on the viscoelastic properties

of the rubber and the parameters of the tribotest, such as load,

sliding velocity, and frequency.10,12 The increase of CoF is

parallel to a progressive increase of the contact depth of the

ball on the DLC coated rubber, indicating an influence of the

viscoelastic properties of the rubber.10

Two friction components can account for the increase of

CoF during a tribotest (see Figure 1). On the one hand, the

adhesive component is related to the adhesive strength

between the surfaces in contact. On the other hand, the visco-

elastic component has its origin in the difference between

the energy consumed on the front part of the ball for deform-

ing the rubber (labeled as Epress in Figure 1) and the energy

recovered on the back part of the ball due to the pushing by

the deformed rubber (labeled as Epush in Figure 1). This hys-

teresis contribution is zero in the case of pure elastic materi-

als due to its immediate recovery.

In previous papers,12,13 the evolution of the viscoelastic

contribution to friction during consecutive cycles was simu-

lated. The steady state is reached when the deformation at a

point on the wear track in a previous pass is recovered in the

next lap. Before reaching this state, the deformation of the

rubber at one point during one pass is not completely recov-

ered during the following lap, and therefore the overall depth

increases. During this period, the viscoelastic contribution to

friction decreases progressively with the number of cycles.

This is a consequence of shape variation of the contact area

between the counterpart and the sample, which leads to a

reduction of the torque opposing to the movement. Thus, the

shape of the front part of the contact area evolves from a cir-

cular shape to a elongated one, which was confirmed experi-

mentally by using ion-etched rubbers.13,14 Nevertheless, the

size of the contact area was observed to grow during the test.

Both results indicate that the adhesive contribution to CoF

should be the origin of the observed frictional behavior,

a)Authors to whom correspondence should be addressed. Electronic mail:

[email protected] and [email protected].

0021-8979/2012/111(11)/114902/6/$30.00 VC 2012 American Institute of Physics111, 114902-1

JOURNAL OF APPLIED PHYSICS 111, 114902 (2012)

Downloaded 04 Jun 2012 to 129.125.63.113. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions

although no experimental validation has been provided yet.

Therefore, the aim of this work is to give an experimental

validation to these theoretical predictions, and to confirm the

nature of the frictional behavior of DLC-protected rubbers.

II. EXPERIMENTAL DETAILS

DLC thin films were deposited on alkyl acrylate copoly-

mer (ACM) rubbers by means of PECVD in a Teer UDP/400

close field unbalanced magnetron sputtering rig, with all the

magnetrons powered off. A pulsed DC (p-DC) power unit

(5 kW Pinnacle Plus, Advanced Energy) was used as sub-

strate bias source, operating at 250 kHz with a pulse-off-time

of 500 ns and voltages between 300 and 600V. Before depo-

sition, the rubber substrates were cleaned by two subsequent

wash procedures using a detergent solution and boiling

water, in order to improve the film adhesion by removal of

the dirt and the wax present on the rubber surfaces,

respectively.8,15

The deposition process was composed by two etching

steps in Ar and Ar/H2 mixtures, respectively, followed by

the deposition in an Ar/C2H2 environment. During these

steps, the temperature of the rubber varied as a result of ions

impingement. Therefore, depending on the bias voltage and

treatment time, the temperature variations during deposition

(DT) can be controlled, and the microstructure of the film

(i.e., the patch size) can be tailored due to the different ther-

mal stresses during the growth.8 The process time was set in

order to obtain a thickness of the DLC film of �300 nm in

all the cases. Further details of deposition can be found

elsewhere.8,9

The microstructure was characterized by scanning elec-

tron microscopy (SEM), using a Philips FEG-XL30 operat-

ing at 3 kV acceleration voltage. Cross sections of DLC film

coated rubber were obtained by fracture after immersion in

liquid nitrogen for 10min. Three-dimensional images were

obtained with a Nanofocus confocal microscope and a Digi-

tal Instruments Nanoscope IIIa atomic force microscopy

operating in tapping mode using a Si tip. The CoFs of the

films were evaluated in a CSM ball-on-disk system operating

against 6 mm diameter 100Cr6 steel balls in air at a relative

humidity of 35%6 2%. In some cases, a ball coated with a

DLC film was used. The test parameters were set to 10 cm/s

of linear speed, test radius between 7 and 13mm, and at least

10 000 laps of sliding distance. Some tests were performed

with oil lubrication, by adding some drops of Shell T9 lubri-

cant on the wear track at the beginning of the tribotest. The

oil was not replenished during the tribotest.

III. RESULTS AND DISCUSSION

The overall CoF observed in this system (l) can be

decoupled into adhesive (lAdh) and hysteresis viscoelastic

(lHyst) contributions as16

l ¼ lAdh þ lHyst: (1)

The adhesive component is mainly related to the adhesion

between two surfaces in contact,16

lAdh ¼A � S

L; (2)

where A is the contact area, S is the shear strength, and L

represents the applied load. Assuming a Hertzian contact and

a circular contact area, we can write

lAdh ¼K1 � L

2=3� S

L¼ KAdhL

ÿ1=3; (3)

where K1 includes geometrical parameters and substrate

properties.

Different approaches can be followed to estimate the

viscoelastic contribution to the CoF.16 In the case where the

substrate is considered as a “matress” formed by Voigt units,

the following expression is obtained:

lHyst ¼ KHyst � L1=2: (4)

Another option is to use a modified elastic model to evaluate

the response of the substrate, which yields to the following

equation:

lHyst ¼ K0

Hyst � L1=3: (5)

It is worth mentioning that, whatever approaches is followed,

the exponent of the load in the viscoelastic contribution to

the CoF is positive, while it is negative in the case of the ad-

hesive one. All the constants (K) in Eqs. (3)–(5) do not

depend on the applied load, but depend on the materials

properties and geometry. Thus, they depend on the lapFIG. 2. Frictional curves for a DLC-covered ACM substrate under three

different loads.

FIG. 1. Scheme of the contributions to friction between a DLC-protected

rubber and the sphere counterpart during a ball-on-disk tribotest.

114902-2 Martinez-Martinez et al. J. Appl. Phys. 111, 114902 (2012)


number, since the viscoelasticity of the substrates causes var-

iations in the depth, size, and geometry of the contact area.

In order to discriminate the viscoelastic and adhesive

contributions, two different experimental strategies have

been applied. The first one consists of using the different

dependences on load of both contributions by performing

dry tribotests under different loads on two different samples.

In the second one, the adhesive strength between the DLC

film and the counterpart is modified while keeping the other

test parameters constant, which will only influence the adhe-

sive component (cf. Eq. (2)).

Figure 2 shows the CoF evolution of the same sample at

three different test loads. It can be seen that the CoF

increases during the test for the three loads. In addition, the

samples tested at higher loads show higher values of CoF.

Figure 3 shows the fitting of the friction coefficient of one

sample tested at different loads to the following expression

(assuming the “mattress” Voigt approach for the hysteresis

contribution, Eq. (4)):

l ¼ KAdh � Lÿ1=3

þ KHyst � L1=2: (6)

Two values of the friction coefficient have been monitored

for each test, the initial and the final ones. In both situations,

the adhesive contribution is much lower than the viscoelastic

one, in contrast to what is observed in non-protected rub-

bers.16 This is because the DLC film significantly reduces

the adhesion between the steel ball and ACM rubber.

Besides, it can be seen that the adhesive component has a

stronger increase than the viscoelastic one when comparing

the initial and final situations. This fact indicates that the

adhesive contribution would be the main responsible of the

overall friction increase during the test.

The values of KAdh and KHyst can be obtained from the

fittings (they correspond to the values of the components

of the fitting functions at 1N load, cf. Eq. (6)). The adhesive-

to-viscoelastic ratio (KAdh/KHyst) is therefore a good parameter

for monitoring the changes of CoF. It can be seen in Figure 4

that this ratio increases from the initial to the steady state, for

two different samples and both models used for the visco-

elastic contribution (cf. Eqs. (4) and (5)). This indicates that

the adhesive contribution to friction increases more than the

viscoelastic one during the test, which supports the previous

observations.

Nevertheless, this method is not so accurate, since the

equations used are too simple to account for the mecha-

nisms involved. For instance, regarding the adhesive contri-

bution, the real contact is non-Hertzian, since the

deformation is not purely elastic, and the contact area is not

circular. Similar simplifications are also used for the visco-

elastic contributions.

Therefore, a second strategy has been followed to inves-

tigate the nature of CoF. Four tribotests have been performed

by varying the shear strength by using two types of balls

(uncoated steel and DLC coated steel), during dry and lubri-

cated tests. These tests have been performed at 1N load and

keeping the other parameters constant on three different sam-

ples: two specimens coated under different conditions

(DT¼ 0 �C and DT¼ÿ94 �C) and an uncoated one for com-

parative purposes. The tests characteristics and average CoFs

(in the last 8000 cycles) are summarized in Table I.

FIG. 3. Fitting of the CoF to the equation (6), at the beginning (a) and at the

end (b) of the tribotests presented in Figure 2.

FIG. 4. Evolution of the adhesive-to-viscoelastic ratio from the beginning to

the end of the tribotest. (a) After using a “mattress” Voigt approach for the

viscoelastic contribution (Eq. (4)). (b) After using a modified elastic

approach for the viscoelastic contribution (Eq. (5)).

TABLE I. Tribotest conditions and CoF of the samples.

Tribotest conditions CoF of different samples

Test diameter (mm) Counterpart material Oil lubrication Uncovered ACM DT¼ 0 �C (smooth) DT¼ÿ94 �C (rough)

26 Steel No 0.7116 0.133 0.2196 0.009 0.1986 0.006

18 DLC No 0.7556 0.055 0.1086 0.002 0.1526 0.004

22 Steel Shell T9 0.0486 0.001 0.0916 0.002 0.1596 0.001

14 DLC Shell T9 0.0486 0.0003 0.0776 0.001 0.1336 0.002



Figure 5 plots the results of the tribotests summarized

in Table I. A large variation of the results can be observed,

which points at an adhesive interaction (see Eq. (2)). The

uncoated rubber without oil lubrication shows a very high

friction (cf. Figure 5(a)), even in the case of sliding against

DLC-coated ball. A very low friction coefficient (ca. 0.048)

is seen with oil lubrication in both cases. In fact, in the case

of steel ball (blue line), a slight decrease of friction coeffi-

cient is seen during the test. This is related to the visco-

elastic contribution to the friction coefficient, which is only

observed in case of a practical lack of adhesive friction and

will be further discussed. Both samples of DLC films

coated ACM rubber show similar behaviors (i.e., curve

shapes) under equivalent test conditions (cf. Figures 5(b)

and 5(c)). The sample prepared at DT¼ÿ94 �C is better in

the case of dry sliding against steel ball, in agreement with

the results reported previously.8,10 While dry sliding against

a DLC coated ball, the friction coefficient is reduced fur-

ther, in agreement with an adhesive mechanism. Neverthe-

less, the CoF keeps growing with increasing number of

cycles. Further, in the case of using a DLC coated ball, a

running-in period is seen for both non-lubricated and lubri-

cated conditions (red and orange lines). This effect is attrib-

uted to a DLC-DLC interaction, and it appears less intense

in the presence of oil lubrication. Both tests with oil lubri-

cation (blue and orange lines) show lower values for the

sample prepared at DT¼ 0 �C, but still higher than the val-

ues observed for the uncoated rubber. This can be explained

by the different nature of the surface of the different

samples.

Figure 6 shows cross section SEM images of the DLC-

protected rubbers. It can be seen that they present a very

different structure, as a consequence of the different temper-

ature variation during the film growth.8,9 The DLC film

deposited at DT¼ 0 �C is more flat, in contrast to the curved

patches of the DLC film grown at DT¼ÿ96 �C. The depth

of these “valleys” has been estimated by means of AFM and

confocal microscopy. Figure 7(a) depicts the top view of the

sample under study, indicating the regions measured by con-

focal microscopy and AFM with squares (see Figures 7(b)

and 7(c)). The silver patches indicated in the image were

used as markers to locate the same region of the sample. The

green line represents the region where the profiles plotted in

Figure 7(d) were taken. It can be seen that the AFM cannot

reach the bottom of the valley due to the limited vertical dis-

placement of the scanning cantilever probe. The confocal

microscopy could reach the bottom of the valley, but only up

to certain points. This is because of the low reflectivity of the

sample, which is even reduced in the case of high slopes

(i.e., the sides of the valley). By combining the data from

both techniques, a valley depth of �4 to �5.5 lm can be esti-

mated in the profiles depicted in Figure 7(d), confirming the

high “roughness” of this sample.

Therefore, the different behavior of the samples under

oil lubrication can be explained as the following (see

sketches in Figure 8). The uncoated ACM rubber appears

relatively smooth and can be covered effectively by an oil

layer (Figure 8(a)). In the case of DLC film deposited at

DT¼ÿ94 �C, as demonstrated previously, the film surface

is formed by curved patches, and the oil cannot fully sepa-

rate the DLC film from the counterpart (Figure 8(c)).

Finally, the sample prepared at DT¼ 0 �C represents an in-

termediate situation (Figure 8(b)). This interpretation is

confirmed by comparing both tests performed with lubrica-

tion on the three samples (cf. Figure 5). In the case of the

uncoated ACM, no difference of CoF is observed between

steel ball or DLC coated steel ball, indicating a good isola-

tion of rubber surface from the counterpart by the oil layer.

In contrast, when the rubber is protected with a DLC film,

FIG. 5. CoF curves in different sliding conditions (see Table I). (a)

Uncoated rubber. (b) Rubber coated with a “smooth” DLC film, deposited at

DT¼ 0 �C. (c) Rubber coated with a “rough” DLC film, deposited at

DT¼ÿ94 �C. The y axis of (b) is the same that in (c).

FIG. 6. Cross section SEM images of the DLC coated rubbers. (a)

DT¼ 0 �C and (b) DT¼ÿ94 �C.



the friction is lower while sliding against the DLC coated

ball as compared to sliding against the steel ball, indicating

a certain interaction with the counterpart. In fact, the reduc-

tion is greater for the “rough” film, confirming a greater

interaction in that case.

The behavior of the different samples against steel ball

in the presence of oil is of particular interest, since it repre-

sents a situation where the adhesive contribution to friction

is minimized. Figure 9 shows the CoF behavior for extended

tribotests up to 30 000 laps. In all cases, the CoF shows a

decreasing behavior with increased number of laps. This

behavior agrees with the expected variation of the visco-

elastic contribution with the number of laps, according to the

theoretical predictions.13

FIG. 7. Characterization of a crack in the sample prepared at DT¼ÿ94 �C. (a) SEM image; (b) confocal image; (c) AFM image; and (d) crack profile. The

squares in the SEM image represent the confocal and the AFM images, and the green line represents the place where the profiles were taken.

FIG. 8. Scheme of the oil distribution for three different situations. (a)

Uncoated rubber. (b) Rubber coated a “flat” DLC film, deposited at

DT¼ 0 �C. (c) Rubber coated with a “rough” DLC film, deposited at

DT¼ÿ94 �C.

FIG. 9. Extended frictional curves of the different samples against steel

counterpart under oil lubrication.



IV. CONCLUSIONS

Two different experiments have been designed to reveal

the nature of the CoF of DLC film-protected rubbers, by

modification of the loads and shear strength between the

surfaces in contact. Under non-lubricated conditions, the

increase of CoF during the tribotests is caused by an

increased adhesive interaction. This is the consequence of

the substrate viscoelasticity, which leads to larger contact

areas at higher number of laps. The viscoelastic contribution

is of secondary importance, and it is only observed when the

adhesive one is minimal. It decreases with the number of

laps, in agreement with the predicted variation of the shape

of the contact area. Finally, a low surface roughness has

been identified as a critical parameter for a more efficient liq-

uid lubrication.

ACKNOWLEDGMENTS

This research was carried out under project number

MC7.06247 in the framework of the Research Program of

the Materials innovation institute M2i (www.m2i.nl).

1J. Robertson, Mater. Sci. Eng. R 37, 129 (2002).2A. Erdemir and C. Donnet, J. Phys. D 39, R311 (2006).3B. J. Hamrock and D. Dowson, Ball Bearing Lubrication. The Elastohy-

drodynamics of Elliptical Contacts (Wiley, 1981).4L. Martinez, R. Nevshupa, L. Alvarez, Y. Huttel, J. Mendez, E. Roman, E.

Mozas, J. R. Valdes, M. A. Jimenez, Y. Gachon, C. Heau, and F. Faverjon,

Tribol. Int. 42, 584 (2009).5T. Nakahigashi, Y. Tanaka, K. Miyake, and H. Oohara, Tribol. Int. 37, 907

(2004).6D. Tsubone, T. Hasebe, A. Kamijo, and A. Hotta, Surf. Coat. Technol.

201, 6423 (2007).7Y. Aoki and N. Ohtake, Tribol. Int. 37, 941 (2004).8D. Martinez-Martinez, M. Schenkel, Y. T. Pei, and J. T. M. De Hosson,

Thin Solid Films 519, 2213 (2011).9D. Martinez-Martinez, M. Schenkel, Y. T. Pei, and J. T. M. De Hosson,

Surf. Coat. Technol. 205, S75 (2011).10M. Schenkel, D. Martinez-Martinez, Y. T. Pei, and J. T. M. De Hosson,

Surf. Coat. Technol. 205, 4838 (2011).11Y. T. Pei, X. L. Bui, and J. T. M. De Hosson, Scripta Mater. 63, 649 (2010).12D. Martinez-Martinez, J. P. van der Pal, Y. T. Pei, and J. T. M. De Hosson,

J. App. Phys. 110, 124906 (2011).13D. Martinez-Martinez, J. P. van der Pal, Y. T. Pei, and J. T. M. De Hosson,

J. Appl. Phys. 110, 124907 (2011).14D. J. Wolthuizen, D. Martinez-Martinez, Y. T. Pei, and J. T. M. De Hos-

son, “Influence of plasma treatments on the frictional performance of rub-

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University of Groningen On the nature of the coefficient of ......although no experimental validation has been provided yet. Therefore, the aim of this work is to give an experimental